Automotive vehicles with convertible tops typically include a storage space in which the top is stowed when fully retracted. The storage space is located behind the passenger compartment. The storage space may be a dedicated space used only for storing the retracted top, or the storage space may be continuous with or part of the trunk space. In either case, it is known to provide a decklid movable to a closed position for concealing the trunk and/or storage space. The decklid is pivotable in a forward direction allowing access to the trunk space and a rearward direction allowing movement of the top in and out of the storage space. A movable tonneau cover is typically used for concealing the top while retracted in the storage space. It remains desirable to provide a control system for coordinating simultaneous or overlapping movement of the decklid, tonneau and/or top so as to minimize the overall cycle time for the top as it moves between extended and retracted positions.